7-spot way

Mar 23, 2010 7:07 AM

These tickets result in lots of 5-spot hits

This week we’ll explore the distribution of ways. The ticket on the left, one of my favorites, has a 5-way-5 and a 5-way-2 spot. The ticket on the right has a 6-way-5 and a 6-way-2 spot. These two tickets offer a good example of why it pays to be careful when constructing a way ticket to play.

Below are the odds for one of hitting each possible catch:

2 2 1 1 1 3 1 1 1 1

1-way-7, 3-way-6, 1-way-7, 4-way-6, 5-way-5, 7-way-4, 6-way-5, 5-way-4, 7-way-3, 5-way-2, 5-way-3, 6-way-2, 3-way-1 4-way-1

7/7 40979.31 40979.31

6/7 1365.977 1365.977

5/7 115.760 115.760

4/7 19.160 19.160

3/7 5.714 5.714

2/7 3.061 3.061

1/7 3.172 3.172

0/7 8.225 8.225

6/6 2957.27 2258.703

5/6 144.876 122.902

4/6 18.226 16.852

3/6 4.531 4.401

2/6 2.076 2.013

1/6 1.823 1.680

0/6 3.896 3.314

5/5 355.458 343.539

4/5 23.340 24.424

3/5 4.267 4.665

2/5 1.822 1.842

1/5 1.377 1.418

0/5 1.943 2.531

4/4 54.982 83.931

3/4 5.908 6.952

2/4 1.777 1.886

1/4 1.229 1.264

0/4 1.358 1.661

3/3 12.953 16.738

2/3 2.019 2.755

1/3 1.185 1.250

0/3 1.131 1.168

2/2 3.931 3.861

1/2 1.190 1.452

0/2 1.025 1.048

1/1 1.713 1.445

0/1 1.014 1.003

Note that although the right hand ticket has one more way five and one more way deuce than the ticket on the left, the odds of hitting a solid five or deuce are not that much better. In fact, if you play the 5-way-5 for \$1 per way, you would expect to hit a 5-spot solid on the average of once every 355 games, or after a gross expenditure of \$1775. If you play the 6-way-5 for \$1 a game, you will expect a solid five on the average of once every 344 games, or after a total gross expenditure of \$2,064. The same comparison holds true of the deuces. You expect to hit a 2-spot after a gross expenditure of about \$20 on the 5-way-2 spot, while it will take nearly \$24 to do the same on the 6-way-2. (When I say gross expenditure, I mean the amount of money played, irrespective of small winners.)

Both tickets will return the same amount of money in the long run, if you play millions of games. This may seem paradoxical at first, because I have just told you that the ticket on the left pays solid hits more often. The explanation is that the right hand ticket offers more chance of multiple winners, more than one solid hit on one catch. It’s just that you have to wait longer for them. This is an important point, because ALL of us operate on finite (limited) bankrolls, and if we play a ticket that pays more often, there is less chance of us going broke!

So here is a little rule of thumb: When you’re playing a mixed group way ticket, a way ticket that consists of different sized groups, you’re better off if you stick to groups that are almost equal in size, rather than one that has widely varying sizes. For example, if you play a 4-way-9, you’re better off playing 5-5-4-4 than 7-7-2-2.

Incidentally, here is one more damning fact about the tickets above: If you hit a six out of seven, you are GUARANTEED at least one or more solid fives on the left hand ticket. This is not so on the right hand ticket, as a cursory examination will reveal!